Example 05.08 Activity Coefficient of the Monomer in a Polymer Using the Athermal
Flory-Huggins Equation
Calculate the activity coefficient of the monomer in a polymer using the athermal Flory-Huggins equation. For the calculation the following volumes should be used:
v1 = 70 cm3/mol v2 = 70000 cm3/mol
general
constants
and
definitions:
Liquid molar volumes of the components
Using equation 5.33, the activity coefficient can be calculated from the volume fractions q of the components in the mixture:
For the activity coefficient, the following expression results:
The surface fraction vector is calculated from the mole fraction vector via:
Simplification of the expression for the activity coefficient leads to:
To avoid the singularity at the pure components, the following function V should be used, which provides identical values without the singularity.
Calculation should be performed for a monomer mole fraction of 0.2:
This results in the following volume fractions:
The following values for the activity coefficients can be found:
The same function can now be used to plot the activity coefficients as function of composition:
Plotting the logarithm of the ratio of the activity coefficients as function of concentration leads to:
The curvature above is very typically for strongly assymetric systems with negative deviation from Raoult's Law.